Select Object randomly from group
Get the group via bpy.data.groups, all objects of that group are accessible via a Group's objects property:

import bpy
import random

group_name = "Group"

group = bpy.data.groups.get(group_name)
assert group is not None

first_ob = group.objects[0]

random_ob = random.choice(group.objects)


If you wanna select another object from a random group the active object is in, use .users_group:

import bpy
from random import choice

scene = bpy.context.scene
ob = bpy.context.object

random_group = choice(ob.users_group)
obs = random_group.objects[:]
obs.remove(ob)

try:
    random_ob = choice(obs)
except IndexError:
    # no other object in chosen group
    pass

#bpy.ops.object.select_all(action='DESELECT')
for ob in scene.objects:
    ob.select = False
random_ob.select = True
bpy.context.scene.objects.active = random_ob